Method and system for evaluating pricing of assets

ABSTRACT

Methods are provided for detecting price manipulation in assets by receiving data indicating returns on an asset, generating a histogram of returns data, determining a first area under a curve of the histogram in a first interval, determining a second area under the curve of the histogram in a second interval; and calculating a bias ratio which comprises a ratio based on the first area and the second area.

PRIORITY APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication No. 60/859,838, filed Nov. 16, 2006, titled Bias RatioMeasuring the Shape of Fraud. The entire contents of that applicationare incorporated herein by reference.

INTRODUCTION

Before purchasing any type of asset, investors typically conduct anassessment of the asset. This assessment typically considers certainstatistics of the asset such as purchase price, historic and predictedreturns, periodic growth, periodic dividends, Sharpe ratios, or otherrelevant statistics. Some assets, such as illiquid assets, can bedifficult to price reliably. In such cases, prices may be obtained fromvarious sources, including multiple dealers. Since each dealer canprovide a different price, and the prices may vary widely, it can bedifficult to establish a true price or other statistic for such assets.

The inventions described herein overcome certain limitations in existingmethods and systems for evaluating pricing of assets.

In one embodiment of the invention, a method is provided comprising:receiving data indicating at least two returns of an asset; generating ahistogram of the returns data; determining a first area under a curve ofthe histogram in a first interval; determining a second area under thecurve of the histogram in a second interval; and calculating a biasratio wherein a numerator comprises at least the first area and adenominator comprises at least the second area. Variations of theembodiment include establishing a benchmark to compare with the biasratio, flagging the asset if the calculated bias ratio exceeds thebenchmark, the first interval is the first standard deviation ofpositive returns and the second interval is the first standard deviationof negative returns, the returns in the first interval are positivereturns and the returns in the second interval are negative returns. Insome embodiments, the bias ratio is an indicator of reliability of thedata and can be calculated using the formula:

${{B\; R} = {{BiasRatio} = \frac{{{Count}\left( r_{i} \right)}:{r_{i}{ɛ\left\lbrack {0,{{+ 1.0}\sigma}} \right\rbrack}}}{{K + {{Count}\left( r_{i} \right)}}:{r_{i}{ɛ\left\lbrack {{{- 1.0}\sigma},0} \right\rbrack}}}}},$

where r₁ is a return and K is a constant, or the formula:

${{B\; R} = \frac{\int_{0}^{1.0\sigma}{r\ {r}}}{K + {\int_{{- 1.0}\sigma}^{0}{r\ {r}}}}},$

where r is a function representing the distribution of returns and K isa constant.

In another embodiment of the invention, a method is provided comprising:calculating a first area of a first interval of a histogram of returnsdata indicating at least two returns of an asset; wherein the returns inthe first interval are positive; calculating a second area of a secondinterval of the histogram of the returns data, wherein the returns inthe second interval are negative; and determining a bias ratio based onthe first area and second area. Variations of the embodiment includethat the bias ratio numerator comprises at least the first area and thebias ratio denominator comprises at least the second area, the firstinterval is a first standard deviation of positive returns and thesecond interval is a first standard deviation of negative returns.

In another embodiment of the invention, a method is provided comprising:receiving data indicating at least two returns of an asset; obtaining afirst count of a number of data in a first interval; obtaining a secondcount of a number of data in a second interval; and calculating a biasratio wherein a numerator comprises the first count and a denominatorcomprises the second count. Variations of the embodiment includeestablishing a benchmark to compare with the bias ratio, flagging theasset if the calculated bias ratio exceeds the benchmark, the firstinterval is a first standard deviation of positive returns and thesecond interval is a first standard deviation of negative returns, andthe returns in the first interval are positive returns and the returnsin the second interval are negative returns.

In another embodiment of the invention, a ratio for verifying an assetreturn is provided comprising: a first area divided by the sum of asecond area and a small, positive constant, the first area and secondarea being areas under a curve of a histogram of asset returns in twoadjacent intervals. Variations of the ratio include that the twoadjacent intervals comprise a first standard deviation of positivereturns and a first standard deviation of negative returns, and thereturns in the first interval are positive returns and the returns inthe second interval are negative returns.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts two histograms of monthly returns;

FIG. 2 depicts a flow diagram of a method according to an embodiment ofthe invention;

FIG. 3 depicts a flow diagram of a method according to anotherembodiment of the invention; and

FIG. 4 depicts a block diagram of a computer system for providing amethod according to an embodiment of the invention.

DETAILED DESCRIPTION

Embodiments of the invention relate to evaluating asset statistics, suchas an asset price or return. Although not specifically described in theexamples, the invention may be equally applied to any type of statisticswhich may be manipulated or for which uncertainties may exist.

Some investment portfolios may not be reliably priced because underlyingassets may not have a definitive market quote and a source of price orother asset data may not be transparent. For such assets, price can beobtained by polling dealers; and the prices received from the dealerscan be used to calculate returns. However, the poll dealer's prices mayvary widely. For example, Table 1 lists the minimum, maximum and averageprices for several quotes obtained on seventeen securities. As indicatedin the last column, the quotes have a range as high as nearly 70%.

TABLE 1 Translucent Pricing MBO—2000 Year End Dealer Quotes # RangeSecurity Quotes Min Avg Max % 1 FHR 2064 G 5 54.31 78.47 85.62 39.90% 2FNR 99-15 SB 4 80.05 86.78 91.25 12.91% 3 FHR 2131 SH 4 73.86 76.2178.18  5.67% 4 FHR 2136 SD 4 74.61 77.84 80.76  7.90% 5 FNR 98-52 SA 578.20 81.57 86.05  9.62% 6 FHR 2156 TS 5 78.94 88.33 94.30 17.39% 7 FHR2138 SB 5 82.36 88.24 92.30 11.26% 8 GNR 00-7 ST 5 98.13 103.88 109.3610.81% 9 FNR 00-6 SK 5 99.30 108.17 115.03 14.55% 10 FHR 2122 SD 5 5.346.05 7.52 35.89% 11 FHR 2138 KS 5 4.73 5.12 6.19 28.36% 12 FHR 2145 MS 53.88 4.61 5.28 30.46% 13 FHR 2136 S 5 5.27 5.77 7.22 33.86% 14 GNR 99-11SC 5 3.77 4.71 5.33 33.21% 15 GNR 99-30 SA 6 4.25 4.87 7.66 69.96% 16GNR 00-1 SD 5 0.58 0.68 0.84 38.78% 17 GNR 99-40 SB 5 1.95 2.36 2.8337.09% Portfolio 4.451 4.970 5.510 21.32% Millions

To price a portfolio, such as one based on the securities listed inTable 1, standard market practice allows a manager to discard any priceoutliers, average the remaining prices of each security, and sum thevalues of the priced securities. Outliers are not necessarily strictlydefined and may be subject to a heuristic rule that “you know it whenyou see it.” Visible outliers may be an indication of the particularsecurity's characteristics and liquidity as well as the marketenvironment in which quotes are solicited, or the outlier may simply bea data error. After discarding outliers, the value of a security may beobtained by averaging the remaining price quotes. The total value of theportfolio, which is referred to as Net Asset Value (“NAV”) is obtainedby summing the individual security values.

NAV is typically calculated at the end of every business day. The changein NAV at the end of a period, such as a month, after adjustment forcapital flows into and out of the fund, determines whether the fund hashad a gain or loss for that period. This determination is critical tothe success of the fund. It is also a determination that can bemanipulated. Consider, for example, one NAV calculation obtained afterdiscarding no outliers (or only some outliers) that results in a smallloss for the period, e.g., −0.01%. A review of the quotes used to obtainthis NAV may show that the pricing calculation included a dealer quotethat was 50% below all the other prices for a particular security.Removing that single quote as an outlier could raise the return for thatperiod to +0.01%. In this scenario, an investment manager can either usethe first calculation (Option 1, in which the outlier was not discarded)resulting in a loss or use the second calculation (Option 2, in whichthe outlier was discarded) showing a gain, and optionally document areason for discarding the outlier.

FIG. 1 depicts two histograms 10 and 20 based on calculations usingOptions 1 (10) and 2 (20). Both histograms plot the number of monthsthat the return on a portfolio fell within one or more standarddeviations (σ) above or below zero. As is well known, the standarddeviation is the root mean square (RMS) deviation of values, in thiscase, the returns, from their arithmetic mean. The smooth histogram 10plots the distribution of returns calculated using Option 1, and thekinked histogram 20 plots the distribution of returns calculated usingOption 2. Since typical investment managers wish to present a fund thathas consistent positive returns, return distributions are oftengenerated along the lines of histogram 20. Calculations using Option 2typically produce more small positive results and fewer small negativereturns than calculations that use Option 1.

As shown in FIG. 1, significant inconsistencies between the plots ofhistograms 10 and 20 are manifested in the hump at the −1.5 StandardDeviation point and in a gap between the two plots in the interval −1σto 0.0. Although calculations using Option 2 compared to Option 1 maynot individually, or collectively, misrepresent return volatility,recent financial history has shown that hiding small losses (bydiscarding certain outliers) can eventually lead to large losses, e.g.,the Sumitomo copper affair as well as the demise of Barings.

The area in the returns histograms of FIG. 1 between the two lines ofhistograms 10 and 20 represents the difference in calculations generatedwith price manipulations. One way to determine whether pricemanipulations have occurred is to model or approximate the area betweenthe two lines. Since this area, in particular, in the interval of thehistogram between −1.0σ and zero can be difficult to model precisely,behavior induced modifications may be manifested in a shape of thereturns histogram in the intervals around zero.

In accordance with one embodiment of the invention, one test fordetecting price manipulation manifested in a returns histogram is acounting test. A flow chart depicting one such test is set forth in FIG.2. As shown in FIG. 2, returns data are received at step 210, and areprocessed at step 220 to obtain a mean and a standard deviation. Next,at step 230, the number of times the return falls within one standarddeviation above zero and the number of times the return falls within onestandard deviation below zero are counted. For example, a first count isobtained for all results in the interval from zero to +1σ, as well as asecond count for all results in the interval from zero to −1σ. A BiasRatio is then obtained at step 240 by forming a quotient from the firstand second counts.

The Bias Ratio is used as an indicator of price manipulation. Typically,higher Bias Ratios indicate that manipulation is likely to haveoccurred. Therefore, a Bias Ratio threshold may be established againstwhich the calculated Bias Ratio is compared at step 250. When the BiasRatio exceeds the threshold, the returns data is flagged as likely tohave been manipulated.

A mathematical formulation for the Bias Ratio is as follows:

Let: [0.0, +1.0σ]=the closed interval from zero to +1 standard deviationof returns (including zero)

Let: [−1.0σ, 0.0)=the half open interval from −1 standard deviation ofreturns to zero (including −1.0σ and excluding zero)

Let: r_(i)=return in month i, 1≦i≦n, and n=number of monthly returns

The Bias Ratio calculated at step 140 is:

${{B\; R} = {{BiasRatio} = \frac{{{Count}\left( r_{i} \right)}:{r_{i}{ɛ\left\lbrack {0,{{+ 1.0}\sigma}} \right\rbrack}}}{{K + {{Count}\left( r_{i} \right)}}:{r_{i}{ɛ\left\lbrack {{{- 1.0}\sigma},0} \right\rbrack}}}}},$

where K is a small, positive, non-zero, constant used to avoid thepossibility of dividing by zero.

While intervals in the above example are standard deviations from [−1.0σto 0) and [0 to +1.0σ], other intervals may be used as will beunderstood by one of skill in the art. In general, the intervals ofinterest are the adjacent intervals on either side of a critical valuein the distribution.

The Bias Ratio approximates a ratio between an area under the returnshistogram immediately above zero and the similar or corresponding areaimmediately below zero. The Bias Ratio typically holds the followingproperties:

-   a. 0≦BR≦n-   b. If r_(i)≦0, ∀ i, then BR=0-   c. If ∀ r_(i) such that r_(i)>0, r_(i)>1.0σ then BR=0-   d. If the distribution r_(i) is Normal with mean=0, the BR→1.0 as    n→∞.

In a second embodiment, shown in the flowchart of FIG. 3, the Bias Ratiois calculated by obtaining an area in two intervals of a returnshistogram. As shown in FIG. 3, returns data is received at step 310, andis processed at step 320 to obtain a mean and a standard deviation. Thereturns data is used to generate a histogram and a distribution functionr is fitted to the histogram data. The area under the distributionfunction is calculated at step 330 for two intervals, one immediatelyabove zero and the other immediately below zero. The Bias Ratio isdetermined at step 340 according to the formula:

${{B\; R} = \frac{\int_{0}^{1.0\sigma}{r\ {r}}}{K + {\int_{{- 1.0}\sigma}^{0}{r\ {r}}}}},$

where K is a small, positive, non-zero, constant used to avoid thepossibility of dividing by zero.

As described previously, the Bias Ratio can be used as an indication ofprice manipulation. Thus, at step 350, the calculated Bias Ratio iscompared with a threshold Bias Ratio and the fund returns are flagged ifthe Bias Ratio exceeds the threshold.

The Bias Ratio defined by a la interval around zero can work well todiscriminate pricing, returns and other statistics among hedge funds.Other intervals may be used to provide metrics with varying resolutions.

Inventions described herein may be automated and used in the exemplarysystem of FIG. 4. As shown, client computers 400 communicate via network410 with a central server 430 which is coupled to one or more databases440, one or more processors 450, and software 460. Other components andcombinations of components may also be used to support Bias Ratio orother calculations described herein as will be evident to one of skillin the art. Server 430 facilitates communication of returns data from adatabase 440 to and from clients 400. Processor 450 providescalculations relevant to calculating a Bias Ratio, or other financialcalculations. Software 460 can be installed locally at a client 400and/or centrally supported for facilitating Bias Ratio calculations andapplications. For example, software 460 may be used in embodiments wherea threshold for a Bias Ratio is established.

Examples of Bias Ratio calculations for indices are presented in Table2. Table 2 includes data relating to numerous indices, including anannualized average return, an associated Sharpe ratio, a StandardDeviation and Bias Ratio. Calculations included in Table 2 are based onmonthly data over a time period greater than 9 years with the exceptionof the Hennessee H.F. High Yield index which includes data spanning 7.5years.

TABLE 2 Bias Ratios: Indices Annualized Average Sharpe Standard BiasIndex (geom) ratio Deviation Ratio NIKKEI 225 Yen Index −3.98 −0.4120.17 1.13 Hennessee H.F. Index EMERGING MKTS 5.93 0.13 13.33 1.28Lehman Aggregate Bond Composite Index 6.80 0.65 4.00 1.36 RUSSELL 20008.76 0.23 19.40 1.36 J P Morgan EMBI + Composite 11.27 0.39 17.99 1.53Lehman Government Index 6.95 0.60 4.57 1.55 MSCI $ World DRI Index 7.190.21 14.42 1.55 S&P 500 DRI 10.35 0.40 15.45 1.56 HENNESSEE H.F. INDEX10.15 0.83 7.13 1.71 Hennessee H.F. INDEX FIXED INCOME 5.73 0.25 6.122.12 CSFB High Yield Index Value 8.21 0.63 6.35 2.15 Lehman AggregateBond - Mortgage Backed Securities Index 6.79 0.83 3.12 2.16 HennesseeH.F. Index HIGH YIELD 4.43 0.03 7.20 2.18 Hennessee H.F. IndexDISTRESSED ONLY 12.28 1.30 6.22 2.61 Hennessee H.F. Index FINANCIALEQUITIES 13.56 0.76 12.30 2.64 Hennessee H.F. Index EVENT DRIVEN 13.131.26 7.10 2.65 Hennessee H.F. Index CONVERTIBLE ARB. 8.83 1.17 3.95 5.00

Generally, assets with a high Sharpe ratio are considered to providegreater return per risk. When compared to the Bias Ratio results ofTable 2, there is a correlation between a high Sharpe ratio and anincreasing Bias Ratio.

Bias Ratios of market and hedge fund indices give some insight into anatural shape of returns near zero. Theoretically, demand for marketswith normally distributed returns around a zero mean may not beexpected. Such markets typically have distributions with a Bias Ratio ofless than 1.0. Major market indices support this trend and have BiasRatios generally greater than 1.0 over long time periods. The returns ofequity and fixed income markets as well as alpha generating strategieshave a natural positive skew of returns which provide a smoothedhistogram as a positive slope near zero. Fixed income strategies with arelatively constant positive return (“carry”) also exhibit total returnseries with a naturally positive slope near zero. Cash investments suchas 90-day T-Bills have large Bias Ratios (i.e., that risk is relativelylow), since they generally do not experience periodic negative returns.Consequently, the Bias Ratio is less reliable for hedge funds that havean unleveraged portfolio with a high cash balance.

Bias Ratios vs. Sharpe ratios

The Sharpe ratio measures risk-adjusted returns, and valuation biasesare expected to understate volatility. An unexpectedly high Sharpe ratiomay be a flag for skeptical practitioners to detect smoothing. (Weisman,Andrew, “Dangerous Attractions: Informationless Investing and Hedge FundPerformance Measurement Bias”, 2002, Journal of Portfolio Management.)Data may not support a strong statistical relationship between a highBias Ratio and a high Sharpe ratio. High Bias Ratios exist in strategiesthat have traditionally exhibited high Sharpe ratios, but many assetshave high Bias Ratios and low Sharpe ratios.

The Bias Ratio and Serial Correlation

Hedge fund investors can use serial correlation (autocorrelation) todetect smoothing in hedge fund returns. Market frictions such astransaction costs and information processing costs that cannot bearbitraged may lead to serial correlation. Stale prices for illiquidassets may have the same effect. Managed prices can also be a cause forserial correlation. As mentioned previously, fund managers of illiquid,hard to price assets, may use some leeway to calculate a fund's NAV.When returns are smoothed by marking securities conservatively in thegood months and aggressively in the bad months a manager may add aserial correlation as a side effect. The more liquid a fund'ssecurities, the less leeway the manager has to make up numbers. (Lo,Andrew W.; “Risk Management For Hedge Funds: Introduction and Overview”,White Paper, June, 2001.)

One common measure of serial correlation is the Ljung-Box Q-Statistic.(Ljung, G. .; Box, G. E. P.; “On a measure of lack of fit in time seriesmodels”, Biometrika, 65, 2, pp. 297-303. 1978.) The p-values of theQ-statistic establish the significance of the serial correlation. (Chan,Nicholas; Getmansky, Mila; Haas, Shane M.; Lo, Andrew; “Systemic Riskand Hedge Funds”, 2005, NBER Draft, August 1, 2005.) The Bias Ratiocompared to the serial correlation metric gives different results. Table3 includes calculations of certain funds, including the Safe Harbor Fundand Bayou Fund, and for each fund, an annualized average, Sharpe ratio,Standard Deviation, Bias Ratio and PVQ6 (a p-value Ljung Box Q Statisticof order 6). The Safe Harbor Fund and Bayou Fund are recent examples offunds that have had valuation problems. (SEC Litigation Release No.18950, Oct. 28, 2004 and SEC Litigation Release No. 19692, May 9, 2006).

TABLE 3 Period: January 1995-November 2005 Annualized Average SharpeStandard Bias Name (geom) Ratio Deviation Ratio PVQ6 Hennessee H.F.Index CONVERTIBLE ARB. 10.24% 1.81 3.55% 3.73 0.00% Sun AsiaOpportunities Fund, LLC 7.86% 0.28 14.48% 1.67 0.02% JASDAQ 5.21% 0.0529.70% 0.84 0.11% Bayou Funds 16.89% 1.21 10.77% 5.54 0.59% Safe HarborFund LP 16.29% 3.03 4.11% 7.00 2.18% Plank Global Value Fund, LP 15.46%1.25 9.31% 2.00 4.72% Sensex - Mumbai Sensex 30 Index 7.66% 0.15 26.02%0.86 4.75% Russell 2000 Value Index 13.20% 0.63 14.96% 1.75 5.25%RUSSELL 2000 11.01% 0.37 19.54% 1.53 10.76% CSFB High Yield Index Value7.96% 0.67 6.16% 2.06 12.24% S&P 500 Total Return 11.49% 0.51 15.16%1.67 71.07% NIKKEI 225 Yen Index −2.55% −0.32 19.62% 1.21 94.56%

Serial correlations appear in many cases that are likely not the resultof willful manipulation but rather the result of stale prices andilliquid assets. Both Sun Asia and Plank (fictitious names are used torepresent real hedge funds) are emerging market hedge funds with NAVsbased on objective prices. However, both funds show significant serialcorrelation. The presence of serial correlation in several marketindices such as the JASDAQ and the SENSEX indicates that serialcorrelation might not be suitable for uncovering price manipulation.However two known problematic funds, namely Bayou, an Equity fund, andSafe Harbor, an MBS fund have relatively high calculated Bias Ratioswhich stand out from Bias Ratios of other funds. In contrast, Sharperatios and PVQ6 for the Bayou fund and Safe Harbor fund do not stand outin comparison with the other funds. Thus, the Bias Ratio provides pricemanipulation indication which other known risk indicators miss.

Benchmark Bias Ratios by Hedge Fund Strategies

Some hedge fund strategy indices may not generate benchmark Bias Ratiosbecause aggregated monthly returns can mask individual manager behavior,e.g., pricing decisions. However, Bias Ratios can be calculated at themanager level and then aggregated to create useful benchmarks.

Variability of Bias Ratios for Different Strategies

Funds that employ illiquid assets can have Bias Ratios that aresignificantly higher than the Bias Ratios of indices representing theunderlying asset class. For example, most equity indices have BiasRatios falling between 1.0 and 1.5. In one sample of funds, equity hedgefunds had Bias Ratios ranging from 0.3 to 3.0 with an average of 1.29and standard deviation of 0.5. On the other hand, the Lehman AggregateMBS Index has a Bias Ratio of 2.16, while MBS hedge funds in the samplehave Bias Ratios from 1.7 to 31.0, with an average of 7.7 and standarddeviation of 7.5. Ceteris paribus, a high Bias Ratio for an equity basedstrategy might be unremarkable for an MBS strategy. Calculations forsuch funds are shown in Table 4:

TABLE 4 Bias Ratio: Strategy Benchmarks Sample Size Average Median 75thPercentile Max Min Stdev MBS 23 7.7 4.0 9.3 31.0 1.7 7.5 Distressed 324.4 3.2 4.6 16.5 1.0 3.8 Convertible 53 3.3 2.7 4.4 10.0 0.6 2.1 Equity133 1.3 1.2 1.6 3.0 0.3 0.5 CTA 46 1.0 1.0 1.2 1.9 0.6 0.3

Uses of the Bias Ratio

Investors ideally examine prices of each individual underlying assetthat comprises a manager's portfolio, or other priced assets. However,in the case of limited price transparency, and time and effort,investors may not have access to price or other statistical information.The Bias Ratio provides an efficient method to highlight pricingproblems. The Bias Ratio can be used to differentiate among a universeof funds and assets. If a fund has a Bias Ratio above a certainbenchmark, median level or other threshold, closer inspection of theassets, pricing policy, and other supporting information may bewarranted; whereas, well below the median might warrant only a cursoryinspection.

The Bias Ratio can also be useful to detect illiquid assetsforensically. For example, if a database search for Long/Short Equitymanagers reveals a fund with a reasonable history and a Bias Ratiogreater than 2.5, detailed diligence will likely reveal some fixedincome or highly illiquid equity investments in the portfolio.

The Bias Ratio can provide an indication of a) illiquid assets in aportfolio combined with b) a subjective pricing policy. Mostvaluation-related hedge fund debacles have exhibited high Bias Ratios.However, the converse may not always be true.

It will be appreciated that the present invention has been described byway of example only, and that the invention is not to be limited by thespecific embodiments described herein. Improvements and modificationsmay be made to the invention without departing from the scope or spiritthereof.

Embodiments of the present invention comprise computer components andcomputer-implemented steps that will be apparent to those skilled in theart. For example, calculations and communications can be performedelectronically, and agreements can be composed, transmitted and executedelectronically.

For ease of exposition, not every step or element of the presentinvention is described herein as part of a computer system, but thoseskilled in the art will recognize that each step or element may have acorresponding computer system or software component. Such computersystem and/or software components are therefore enabled by describingtheir corresponding steps or elements (that is, their functionality),and are within the scope of the present invention.

1.-22. (canceled)
 23. A system comprising: memory operable to store atleast one program; and at least one processor communicatively coupled tothe memory, in which the at least one program, when executed by the atleast one processor, causes the at least one processor to: receive dataindicating at least two returns of an investment portfolio comprisingone or more assets, said returns being calculated on a periodic basisand indicating a gain or loss for the investment portfolio for eachperiod; generate a histogram of the returns data by plotting the returnsdata on one axis of the histogram against a standard deviation of thereturns data on a second axis of the histogram; determine a first areaunder a curve of the histogram in a first interval comprising a productof a positive standard deviation of the returns; determine a second areaunder the curve of the histogram in a second interval comprising aproduct of a negative standard deviation of the returns; calculate abias ratio wherein a numerator of the bias ratio comprises the firstarea and a denominator of the bias ratio comprises the second area; andanalyze the calculated bias ratio to determine reliability of thereturns data wherein the bias ratio is calculated using the formula:${{B\; R} = {{BiasRatio} = \frac{{{Count}\left( r_{i} \right)}:{r_{i}{ɛ\left\lbrack {0,{{+ X}\; \sigma}} \right\rbrack}}}{{K + {{Count}\left( r_{i} \right)}}:{r_{i}{ɛ\left\lbrack {{{- X}\; \sigma},0} \right)}}}}},$where r_(i) is a return, σ represents standard deviation, X is apositive, non-zero value, K is a positive, non-zero constant, and εindicates that r_(i) is within the closed interval [0,+Xσ] in the caseof the numerator and within the half open interval [−Xσ,0) in the caseof the denominator.
 24. A system comprising: memory operable to store atleast one program; and at least one processor communicatively coupled tothe memory, in which the at least one program, when executed by the atleast one processor, causes the at least one processor to: receive dataindicating at least two returns of an investment portfolio comprisingone or more assets, said returns being calculated on a periodic basisand indicating a gain or loss for the investment portfolio for eachperiod; generate a histogram of the returns data by plotting the returnsdata on one axis of the histogram against a standard deviation of thereturns data on a second axis of the histogram; determine a first countof a number of data in a first interval comprising a product of apositive standard deviation of the returns; determine a second count ofa number of data in a second interval comprising a product of a negativestandard deviation of the returns; and calculate a bias ratio wherein anumerator of the bias ratio comprises the first count and a denominatorof the bias ratio comprises the second count; and analyze the calculatedbias ratio to determine reliability of the returns data wherein the biasratio is calculated using the formula:${{B\; R} = {{BiasRatio} = \frac{{{Count}\left( r_{i} \right)}:{r_{i}{ɛ\left\lbrack {0,{{+ X}\; \sigma}} \right\rbrack}}}{{K + {{Count}\left( r_{i} \right)}}:{r_{i}{ɛ\left\lbrack {{{- X}\; \sigma},0} \right)}}}}},$where r_(i) is a return, σ represents standard deviation, X is apositive, non-zero value, K is a positive, non-zero constant, and εindicates that r_(i) is within the closed interval [0,+Xσ] in the caseof the numerator and within the half open interval [−Xσ,0) in the caseof the denominator.
 25. The system of claim 23 wherein one or more ofthe one or more assets in the investment portfolio are valued withreference to subjective criteria.
 26. The system of claim 24 wherein oneor more of the one or more assets in the investment portfolio are valuedwith reference to subjective criteria.
 27. A system comprising: memoryoperable to store at least one program; and at least one processorcommunicatively coupled to the memory, in which the at least oneprogram, when executed by the at least one processor, causes the atleast one processor to: receive data indicating at least two returns ofan investment portfolio comprising one or more assets, said returnsbeing calculated on a periodic basis and indicating a gain or loss forthe investment portfolio for each period; generate a histogram of thereturns data by plotting the returns data on one axis of the histogramagainst a standard deviation of the returns data on a second axis of thehistogram; determine a first area under a curve of the histogram in afirst interval comprising a product of a positive standard deviation ofthe returns; determine a second area under the curve of the histogram ina second interval comprising a product of a negative standard deviationof the returns; calculate a bias ratio wherein a numerator of the biasratio comprises the first area and a denominator of the bias ratiocomprises the second area; and analyze the calculated bias ratio todetermine reliability of the returns data wherein the bias ratio iscalculated using the formula:${{B\; R} = \frac{\int_{0}^{X\; \sigma}{r\ {r}}}{K + {\int_{{- X}\; \sigma}^{0}{r\ {r}}}}},$where r is a function representing a distribution of returns (dr), σrepresents standard deviation, X is a positive, non-zero value, and K isa positive, non-zero constant.
 28. A system comprising: memory operableto store at least one program; and at least one processorcommunicatively coupled to the memory, in which the at least oneprogram, when executed by the at least one processor, causes the atleast one processor to: receive data indicating at least two returns ofan investment portfolio comprising one or more assets, said returnsbeing calculated on a periodic basis and indicating a gain or loss forthe investment portfolio for each period; generate a histogram of thereturns data by plotting the returns data on one axis of the histogramagainst a standard deviation of the returns data on a second axis of thehistogram; determine a first count of a number of data in a firstinterval comprising a product of a positive standard deviation of thereturns; determine a second count of a number of data in a secondinterval comprising a product of a negative standard deviation of thereturns; and calculate a bias ratio wherein a numerator of the biasratio comprises the first count and a denominator of the bias ratiocomprises the second count; and analyze the calculated bias ratio todetermine reliability of the returns data wherein the bias ratio iscalculated using the formula:${{B\; R} = \frac{\int_{0}^{X\; \sigma}{r\ {r}}}{K + {\int_{{- X}\; \sigma}^{0}{r\ {r}}}}},$where r is a function representing a distribution of returns (dr), σrepresents standard deviation, X is a positive, non-zero value, and K isa positive, non-zero constant.
 29. The system of claim 27 wherein one ormore of the one or more assets in the investment portfolio are valuedwith reference to subjective criteria.
 30. The system of claim 28wherein one or more of the one or more assets in the investmentportfolio are valued with reference to subjective criteria.